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Simplifying 16x2 + 3x + -160 = 0 Reorder the terms: -160 + 3x + 16x2 = 0 Solving -160 + 3x + 16x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -10 + 0.1875x + x2 = 0 Move the constant term to the right: Add '10' to each side of the equation. -10 + 0.1875x + 10 + x2 = 0 + 10 Reorder the terms: -10 + 10 + 0.1875x + x2 = 0 + 10 Combine like terms: -10 + 10 = 0 0 + 0.1875x + x2 = 0 + 10 0.1875x + x2 = 0 + 10 Combine like terms: 0 + 10 = 10 0.1875x + x2 = 10 The x term is 0.1875x. Take half its coefficient (0.09375). Square it (0.0087890625) and add it to both sides. Add '0.0087890625' to each side of the equation. 0.1875x + 0.0087890625 + x2 = 10 + 0.0087890625 Reorder the terms: 0.0087890625 + 0.1875x + x2 = 10 + 0.0087890625 Combine like terms: 10 + 0.0087890625 = 10.0087890625 0.0087890625 + 0.1875x + x2 = 10.0087890625 Factor a perfect square on the left side: (x + 0.09375)(x + 0.09375) = 10.0087890625 Calculate the square root of the right side: 3.163667028 Break this problem into two subproblems by setting (x + 0.09375) equal to 3.163667028 and -3.163667028.Subproblem 1
x + 0.09375 = 3.163667028 Simplifying x + 0.09375 = 3.163667028 Reorder the terms: 0.09375 + x = 3.163667028 Solving 0.09375 + x = 3.163667028 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.09375' to each side of the equation. 0.09375 + -0.09375 + x = 3.163667028 + -0.09375 Combine like terms: 0.09375 + -0.09375 = 0.00000 0.00000 + x = 3.163667028 + -0.09375 x = 3.163667028 + -0.09375 Combine like terms: 3.163667028 + -0.09375 = 3.069917028 x = 3.069917028 Simplifying x = 3.069917028Subproblem 2
x + 0.09375 = -3.163667028 Simplifying x + 0.09375 = -3.163667028 Reorder the terms: 0.09375 + x = -3.163667028 Solving 0.09375 + x = -3.163667028 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.09375' to each side of the equation. 0.09375 + -0.09375 + x = -3.163667028 + -0.09375 Combine like terms: 0.09375 + -0.09375 = 0.00000 0.00000 + x = -3.163667028 + -0.09375 x = -3.163667028 + -0.09375 Combine like terms: -3.163667028 + -0.09375 = -3.257417028 x = -3.257417028 Simplifying x = -3.257417028Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.069917028, -3.257417028}
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